The Morphology of ULF Waves in the Earth's Foreshock

G. Le and C. T. Russell
Institute of Geophysics and Planetary Physics, University of California
at Los Angeles

Abstract. The Earth's foreshock is the region upstream from the bow shock where
the interplanetary magnetic field intersects the bow shock. It is
characterized by backstreaming electrons and ions, as well as associated
electrostatic and electromagnetic waves over a wide frequency range. One
class of upstream electromagnetic waves, large-amplitude compressional
ULF waves in the ion foreshock region, has long been postulated as a
major source of magnetospheric ULF waves. In this paper, we discuss
recent observations of properties
of ULF waves. First the
general morphology of the foreshock at different IMF orientations and
the
different types of ULF waves are reviewed. Then observations of critical
wave properties of importance to the Earth's magnetosphere,
such as frequency, bandwidth, coherence length and spatial
evolution in the foreshock, are discussed.

1. INTRODUCTION

The generation of upstream waves, especially the ultra-low-frequency
(ULF) waves, in planetary foreshocks is both an active and an important
topic of space plasma physics investigations. These waves are
ubiquitous, having been observed in front of the bow shock of all of
the planets and in front of comets Halley and Giacobini-Zinner. They
modify both the solar wind and the turbulence spectrum convected to the
Earth's magnetosphere, altering the nature of the shock jump, the
pressure fluctuations on the magnetopause and ultimately the spectrum of
waves in the magnetosphere. Moreover, these foreshock waves lead to the
acceleration of some particles to very high energies by means of
wave-particle interactions and provide us with a testbed in which to
study processes thought to be responsible for the acceleration of cosmic
ray particles. Finally, the instabilities which drive these waves and
the processes associated with the waves provide an excellent test of the
basic theories of waves and instabilities in plasma physics.

Upstream waves have been found in front of the bow shocks of all of the
planets visited to date. Terrestrial upstream waves have been studied
extensively by many authors and much of the early work has been well
documented in the 1 June, 1981 special issue of J. Geophys. Res..
Upstream waves have also been investigated at Mercury by Fairfield and
Behannon [1976] and Orlowski et al. [1990]; at Venus by Hoppe and
Russell [1982] and Orlowski and Russell [1991]; at Mars by Russell et
al. [1990a]; at Jupiter by Smith et al. [1983] and Goldstein et al.
[1985]; at Uranus by Russell et al. [1990b], Smith et al. [1989] and
Zhang et al. [1991a]; and at Neptune by Zhang et al. [1991b]. Based on
the early work, as reviewed by Russell and Hoppe [1983], we have
developed a picture of the morphology of the upstream wave region. In
that picture, wave and particle phenomena upstream of the shock arise
from kinetic effects occurring in the shock transition region (see
Sonnerup [1969]; Paschmann et al. [1980]; Armstrong et al. [1985];
Scholer [1985]; Gosling and Robson [1985] and references therein]. These
effects include: reflection, shock drift acceleration, and heating of
post-shock plasma. The effectiveness of the above mechanisms as well as
the characteristics of the backstreaming populations (at the shock) are
strongly dependent on the direction of the shock normal relative to the
plasma flow and the interplanetary magnetic field (IMF) orientation.

For a stationary IMF we are able to define regions (in the shock frame)
with characteristic backstreaming populations.
Figure 1
shows a
schematic of the foreshock geometry. First we can divide the unshocked
plasma into two regions, one magnetically unconnected where no IMF lines
connect to or cross the shock and one so-called magnetic foreshock
region where all IMF lines are connected to the bow shock. The IMF lines
tangent to the bow shock form the boundary between those two regions.
The superposition of the upstream motion along the magnetic field line
and the convection associated with the interplanetary electric field,
results in the formation of electron and ion foreshocks within the
region of unshocked solar wind connected to the bow shock. Because of
the finite velocity of these backstreaming particles and the convection
associated with the interplanetary electric field, the electron and
proton foreshocks do not fill the entire magnetically connected region,
nor are they fully coincident. Moreover, the properties of the waves and
plasma are position dependent within the foreshock.

The electron foreshock boundary is defined by the fastest electrons
accelerated along the tangent magnetic field lines. Since the convection
velocity is small compared to the typical bulk velocity of escaping
electrons (which can be many times of their thermal velocity) the
electron foreshock boundary is only slightly displaced relative to the
IMF tangent lines. A variety of associated waves has been found in the
electron and ion foreshocks [Hoppe et al., 1981]. In the electron
foreshock in addition to electrostatic (Langmuir) mode [Gurnett, 1985]
an electromagnetic mode at ULF frequencies has also been identified: the
so-called one-Hertz whistlers [Russell et al., 1971; Fairfield, 1974;
Hoppe et al., 1981, 1982]. One example of one-Hz waves is shown in
Figure 2(a).

The ion foreshock boundary in contrast appears to be defined by
position-dependent acceleration processes that do not allow protons to
move upstream (in the shock frame) until some distance downstream of the
electron foreshock [Thomsen, 1985]. It is located much deeper in the
magnetic foreshock, beginning close to the region called the
quasi-parallel part of the bow shock. Studies of the ISEE 1 and 2 data
have revealed that the ion foreshock in turn can be divided into three
regions characterized by beam-like, intermediate and/or gyrating, and
diffusive ion distributions depending on the local Bn, the angle between
the IMF and the bow shock normal [Gosling et al., 1978; Paschmann et
al., 1979, 1981]. ULF waves in the ion foreshock have been observed at
frequencies below the proton gyrofrequency [Greenstadt et al., 1968;
Russell et al., 1971; Hoppe et al., 1981; Le et al., 1992]. These
observations revealed several types of ULF waves in the ion foreshock:
sinusoidal waves, shocklets and discrete wave packets, and three-second
waves. Figure 2(b) shows an example of low-frequency waves which are
nearly sinusoidal. They typically have amplitudes of a few nT, are
primarily transverse, and exhibit predominantly left-handed polarization
in the spacecraft frame. ULF waves in the ion foreshock are most
frequently observed in large-amplitude, highly compressional forms. They
steepen into small shocklike waveform and have been called shocklets.
Discrete wave packets, which have higher frequency, are often associated
with the steepening edges of the shocklets, as shown in Figure 2(c).
Another type of foreshock waves has frequency near three seconds and is
always right-handed and nearly circularly polarized in the spacecraft
frame. One example of three-second waves is shown in Figure 2(d).

One type of upstream ULF waves, the large-amplitude compressional waves,
is particularly important to the Earth's magnetosphere. These waves must
propagate obliquely with respect to the magnetic field since they are
highly compressional. Since they were first observed by Greenstadt et
al. [1968] and Fairfield [1969], several generation mechanisms related
to electromagnetic ion/ion instabilities from linear theory have been
proposed to explain the source of these waves [Gary, 1991]. The
backstreaming ions have a density of ~ 1% of the solar wind density.
Their bulk velocities range from the order of the Alfven velocity (~
50 km/sec at 1 AU) for diffuse ions to the order of solar wind speed for
intermediate, gyrating and beam-like ions [cf. Thomsen, 1985 for a
review]. Under these conditions, the most obvious instability is the
anomalous Doppler-shifted ion/ion resonant instability, in which the
right-handed polarized waves (fast magnetosonic mode) resonate with the
backstreaming ion beam [Barnes, 1970; Gary, 1978; Sentman et al., 1981].
This instability generates right-handed waves in the upstream region
which propagate in the same direction as the beams (upstream) in the
solar wind frame. Since they are convected downstream by the solar wind
flow, they will be Doppler-shifted to left-handed waves in the
spacecraft frame. When the backstreaming ions are sufficiently fast (Vb
> 10 VA) and dense (Nb ~ 10% of solar wind density), besides the above
resonant instability, the non-resonant firehose-like instability will
excite ULF waves in the right-handed magnetosonic branch which propagate
in the direction opposite to the ion beam, i.e., downstream toward the
bow shock. These waves are also right-handed in the spacecraft reference
frame. Gary et al. [1984] have shown that the non-resonant instability
has larger growth rate than the resonant instability if Vb/VA and Nb/Nsw
are sufficiently large. In another extreme case when the backstreaming
ions are extremely hot with thermal speeds greater than their streaming
velocity (Vth > Vb), the left-handed Alfven/ion resonant mode is also
unstable. The growth rate for the two resonant instabilities can be
comparable [Sentman et al., 1981; Gary, 1985]. This left-handed resonant
instability generates waves propagating upstream from the bow shock and
will be Doppler-shifted to right-handed waves in the spacecraft frame as
they are convected downstream by the solar wind. Thus, according to
linear theory, the upstream ULF waves will be more often left-handed in
the spacecraft frame under typical conditions and also can be
right-handed in the spacecraft frame under extreme conditions of fast,
dense beams or hot beams. However, when the waves are right-handed in
the spacecraft frame, they can be intrinsically either right-handed
magnetosonic mode or left-handed Alfven mode in the solar wind frame.
Observations have shown that the left-handed ULF waves (in the
spacecraft frame) are indeed the dominant mode in the foreshock region
[Hoppe et al., 1981; Hoppe and Russell, 1983]. They have frequencies of
~ 0.1 ( is the local ion cyclotron frequency) and wavelengths of
the order of 1 Re. For the right-handed waves (in the spacecraft
frame), their intrinsic modes have not been identified.

One important fact of obliquely propagating magnetosonic waves is that
there is a first-order density perturbation associated with the magnetic
perturbation. In the MHD limit, the density and magnetic perturbation
for a magnetosonic waves propagating at an angle are related by
[Siscoe, 1983]:

where is the perturbation in plasma number density,
is the
perturbation in field strength, is the wave phase velocity and
is the sound speed in the plasma. From the equation, we note that
the , the relative perturbation in density, is always greater or
equal to , the relative field perturbation, since
for fast magnetosonic waves.
For upstream waves which are strongly compressional, the density
fluctuations associated with the waves are very significant as they
cause large fluctuations in solar wind dynamic pressure.

Observations show that the ULF waves generated in the region upstream of
the bow shock are convected downstream by the solar wind flow because
their group velocity is much smaller than the solar wind flow speed
[Hoppe et al., 1981; Hoppe and Russell, 1983]. The downstream convection
of compressional ULF waves can have a profound impact on the Earth's
magnetosphere. The upstream fluctuations associated with these waves are
carried downstream along solar wind streamlines into the magnetosheath.
The streamlines in the magnetosheath which approach most closely to the
magnetopause pass through the subsolar region of the bow shock. During
intervals when the IMF cone angle is small ( < 45 deg), these waves fill the
subsolar upstream region, as illustrated in
Figure 3
(adapted from
Russell et al. [1983]). Under the condition of small IMF cone angle, the
solar wind carries the upstream ULF fluctuations to the magnetopause
boundary. The magnetopause responds to these pressure fluctuations and
transfers wave energy into the dayside magnetosphere. The waves on the
magnetopause can excite field line resonances in the magnetosphere, as
described by Southwood [1974] and Chen and Hasegawa [1974]. Although
the process by which the energy enters into the magnetosphere is still
not well understood, it has been generally agreed that upstream waves
are a major source for dayside Pc 3 and 4 magnetic pulsations in the
Earth's magnetosphere (cf. Odera, [1986] for a review).

There is much observational evidence to support this idea. Many studies
of the magnetic pulsations in the dayside magnetosphere have indicated
that their occurrence is controlled by the IMF cone angle [eg.
Troitskaya et al., 1971; Russell et al., 1983; Yumoto et al., 1985;
Engebretson et al., 1986, 1987; Yumoto, 1988]. Luhmann et al. [1986]
found that magnetosheath turbulence is sensitive to the IMF cone angle
and is enhanced in the subsolar region during periods of small cone
angles. By using multiple spacecraft observations, Engebretson et al.
[1991] found on a case-by-case basis that small cone angles are well
correlated with large turbulence in the magnetosheath and the
simultaneous excitation of Pc 3 and 4 pulsations in the dayside outer
magnetosphere. Other evidence is that the frequencies of both upstream
and magnetospheric ULF waves have a similar dependence on the IMF
strength, as shown in
Figure 4
(adapted from Russell and Hoppe [1981]).
In Figure 4, the solid circles and solid lines are from observations of
upstream ULF waves. Dashed, dash-dot, and dotted lines are from
observations of ground-based Pc 3-4 waves as given by Gul'yel'mi et al.
[1973], Gul'yel'mi [1974], and Gul'yel'mi and Bol'shakova [1973],
respectively.

In this paper, we discuss recent advances in the understanding of the
foreshock ULF morphology and wave properties, as well as remaining
problems. We present our studies of critical upstream ULF wave
properties of importance to the magnetospheric ULF waves.

2. GEOMETRY OF ULF FORESHOCK

The schematic of the foreshock in Figure 1 shows that its geometry
depends mainly on the IMF cone angle. The first requirement in studying
the general morphology of the foreshock is to quantitatively determine
the upstream boundary of the ULF foreshock for different IMF cone
angles. This boundary represents the motion of backstreaming ions in
the foreshock region since the ULF waves are the consequences of
instabilities
generated by these backstreaming ions. If the ions originating in the
bow shock have velocity components upstream away from the bow shock, the
ions will leave the bow shock with the equation of motion to the first
order as:

where B is the IMF, is the ion gyrofrequency,
and -Vsw x B is the solar
wind convection electric field. The above equation shows that the motion
of backstreaming is confined in the plane containing the solar wind flow
and the IMF, called V-B plane. The ions' net guiding center velocity in
the V-B plane is the vector sum of parallel velocity along the IMF
upstream and the downstream E x B drift:

V = V// + Vd

as shown in Figure 1. The ion foreshock boundary in the V-B plane is
parallel to the guiding center velocity [Greenstadt, 1976]. But the
starting point of the foreshock boundary on the bow shock is controlled
largely by , the angle between the IMF and the local bow shock normal,
because controls the ion reflection process. In the case of small ,
or quasi-parallel shock, the guiding center velocity makes a large angle
to the bow shock surface, and thus, particles can leave the bow shock
very easily. On the other hand, if is very large, or
quasi-perpendicular shock, the gyromotion of the ions around the
magnetic field lines may bring the ions back to the bow shock before
they finish one gyration around the magnetic field line if their pitch
angles are appropriate. Gosling et al. [1982] have demonstrated that the
reflected ions can escape upstream only when < 45 deg in the case of
specular reflection.

The pioneering work of locating the ULF foreshock boundary can be found
in Greenstadt et al. [1970] and Greenstadt [1972], in which this
boundary was determined based on detailed case studies. Later this
boundary was determined statistically by Greenstadt and Baum [1986], in
which they used the ISEE 1 magnetometer data to find actual crossings of
the ULF foreshock boundary.
Their study clearly showed the IMF cone angle control of the ULF
foreshock boundary. They displayed the locations of ISEE 1 at ULF
foreshock boundary crossings in the V-B plane for moderate cone angles
of 40-50 deg and for small cone angles of 20-30 deg. They found that the
patterns of the scatter plots of the crossings defined a boundary for
each of the two subsets, but the slopes of the two boundaries are
different. The ULF wave foreshock boundary determined in this study also
inferred the backstreaming ion velocity of 1.6Vsw.

In our recent study of determining the ULF foreshock boundary, we
identified many foreshock boundary crossings in the upstream region
when the IMF cone angle was nearly constant for extended time periods
and thus the foreshock boundary was steady in space [Le
and Russell, 1992a]. The work consisted of two steps, first to determine
of the ULF foreshock on the bow shock, and second to determine the
slope of the ULF foreshock boundary. In the first step, we examined ISEE
bow shock crossings at various positions to determine the source point
on the bow shock which separated disturbed (with ULF waves) and
undisturbed (without ULF waves) upstream magnetic field. The statistical
study of the bow shock crossings showed that the ULF foreshock started
at ~ 50 deg . In the second step, we found that the ULF foreshock
boundary was less sensitive to small changes of the IMF direction at
larger cone angle. The ULF foreshock boundary was well defined in the
V-B plane for cone angles > 40 deg.
Figure 5
shows the ISEE positions in the
V-B plane for five ULF foreshock boundary crossings identified at 50 +/- 5 deg
IMF cone angles. The bow shock was scaled by the solar wind dynamic
pressure and Mach number, and then, normalized to the same size for each
crossing. The spacecraft positions form a clear boundary in the V-B
plane. From this boundary, we infer that the backstreaming ions had a
velocity of 1.3Vsw along the IMF and a net guiding center velocity of
1.5Vsw in the Earth's frame. On average, the ULF foreshock boundary
corresponds to the trajectory of backstreaming ions with a streaming
velocity of ~ 1.4Vsw along the IMF in the Earth's frame and a source
point at ~ 50 deg when the IMF cone angle is moderate
( > 40 deg). When the IMF cone angle is small (20 < < 30 deg), the ULF foreshock
boundary is not well defined.

3. ULF WAVES FOR RADIAL IMF

The foreshock geometry for nearly radial IMF is different from that at
moderate and large cone angles. The solar wind convection electric field
is very small and the backstreaming ions move along the magnetic field
in a nearly flow-aligned IMF condition. It is the most favorable
condition for the generation of upstream waves since the particles can
go upstream more easily from the bow shock. In this case, most of the
day side upstream region is inside the ion foreshock region, although it
is still not clear if there is a distinct boundary which separates the
ULF foreshock from the undisturbed solar wind. We emphasize that the
large-amplitude ULF waves for nearly radial IMF can be convected close
to the Earth's magnetosphere under this IMF configuration. Observations
also show that it is the most favorable geometry for the occurrence of
magnetospheric ULF waves [Russell et al., 1983].

ULF waves observed for nearly radial IMF are typically in the form of
steepened shocklets which sometimes have discrete wave packets at the
steepening edges.
Figure 6
shows examples of ULF waves for nearly radial
IMF where each panel consists of 10 minutes of high resolution data
within an interval of cone angle < 10 deg which lasted at least one hour.
These waves are similar in form to those observed well downstream from
the foreshock boundary at moderate and large cone angle. As shown in
Figure 7,
the ULF wave region extends upstream with a scale length of
~ 23 Re for this geometry. The top panel of Figure 7 shows the
normalized ULF wave spectral amplitude as a function of distance from
the bow shock along the IMF, which is roughly the same as distance from
bow shock along Sun-Earth line for nearly radial IMF. The bottom panel
of Figure 7 shows the spatial coverage of these data in the plane which
contains the spacecraft and the Sun-Earth line (there is no meaningful
V-B plane for nearly radial IMF). Although there is a tendency of
decreasing wave amplitude with increasing distance from the bow shock,
the decrease of the amplitude is very slow with a scale of ~ 23 Re.
Ipavich et al. [1981] found that the upstream 30 keV proton intensity
varied exponentially with the radial distance from the bow shock and had
a scale length of 7 +/- 2 Re. The IMF direction during the time of peak
intensity was within ~ 15 deg of the radial direction for 90% of their
events. The two scale lengths are qualitatively consistent to the extent
that the upstream particles may have different scale lengths at
different energies and the correlation between the beam density and wave
amplitude is not exactly linear.

Right-handed polarized waves (in the spacecraft frame) are more
frequently observed at nearly radial IMF than at moderate and large cone
angles. Under conditions typical of the ion foreshock, the most unstable
mode is the right-handed polarized magnetosonic wave due to the resonant
instability [Barnes, 1970; Gary, 1978]. These waves will be
Doppler-shifted to left-handed polarizations in the spacecraft frame.
Left-handed ULF waves (in the spacecraft frame) are indeed the dominant
mode observed in the upstream region [Hoppe et al., 1981; Hoppe and
Russell, 1983]. However both left-handed and right-handed modes are
observed with equal probability for nearly radial IMF and their
ellipticity seems to be correlated with the wave amplitude.
Figure 8
shows the wave ellipticity versus the normalized wave amplitude.
Negative ellipticity indicates left-handed polarization in the
spacecraft frame and positive ellipticity corresponds to right-handed
polarization in the spacecraft frame. There is a positive correlation
between the ellipticity and the wave amplitude with a correlation
coefficient of 0.57. A similar correlation between ellipticity and wave
amplitude has been reported by Russell et al. [1987] for moderate IMF
cone angles. The right-handed waves are stronger than the left-handed
waves (in the spacecraft frame).

The correlation between polarization and amplitude suggests that
different mechanisms generate waves with different amplitudes. As we
discussed in the introduction, according to linear theory, the
left-handed polarized waves in the spacecraft frame are favored under
typical backstreaming ion condition (Nb ~ Nsw, Vb < 10 VA) via the
ion/ion right-handed resonant instability. When the backstreaming ions
are very dense and fast (Nb ~ 10 Nsw, Vb > 10 VA) or very hot (Vth >
Vb), right-handed polarized waves are observed in the spacecraft frame,
that are generated either by the ion/ion nonresonant instability or the
ion/ion left-handed resonant instability. The facts 1) that right-handed
waves in the spacecraft frame are more often observed and 2) that these
waves are stronger for nearly radial IMF suggest that this upstream
configuration is a favorable condition for faster and denser ion beams
(nonresonant instability) or hotter ion beams (resonant instability).
Energetic particle observations have shown that the upstream ions are of
diffuse type and have small bulk velocity under radial IMF [Ipavich et
al., 1981]. It seems that the nonresonant instability can be dismissed.
However, this is just speculation since little has been done to identify
the intrinsic mode for the waves which have right-handed polarization in
the spacecraft frame.

4. PROPERTIES OF UPSTREAM WAVES RELEVANT TO ULF WAVES IN THE
MAGNETOSPHERE

Compressional ULF waves are an intrinsic feature of quasi-parallel
shocks. Their existence in front of the bow shock modifies both the
solar wind and the turbulence spectrum convected downstream to the
magnetopause. In this section, we review recent observations of the wave
properties, especially those of importance to the Earth's magnetosphere,
including the magnitude of the pressure fluctuations associated with the
waves, the coherence length, and the bandwidth.

Pressure Fluctuations Associated with the Waves

MHD theory predicts that ULF waves cause significant density
fluctuations, and thus dynamic pressure fluctuations as well in the
unshocked solar wind. Although the fluctuating magnetic field of these
waves is the most readily measured aspect of the waves, it is the
associated pressure fluctuations which can cause the magnetopause to
oscillate in response to the waves. Observations show that density and
dynamic pressure fluctuations have been significantly enhanced in the
ULF foreshock [Paschmann et al., 1979; Bame et al., 1980; Le, 1991]. The
density and dynamic pressure fluctuations associated with the ULF waves
are ~ 20% of the average background value. In comparison,
fluctuations in the undisturbed solar wind at these frequencies are only
~ 5% of the background average.

Figure 9
shows an example of how the ULF foreshock can modify the solar
wind itself. It contains 5 hours data from the ISEE 1 magnetometer and
Cross-Fan Solar Wind Experiment, including magnetic field, solar wind
ion density, bulk velocity and dynamic pressure in the upstream region.
As already noted, the foreshock geometry is very sensitive to the IMF
direction. When the IMF changes its direction, the spacecraft may
suddenly find itself located inside the foreshock region. In Figure 9,
the IMF changes its direction as well as magnitude near 0825UT.
Following the onset of the ULF waves, enhanced fluctuations in solar
wind ion density, ion bulk velocity and dynamic pressure
()
are present that are clearly associated with the ULF waves. The bulk of the
solar wind is also slowed down (by ~ 38 km/sec in this example) in
the foreshock region. Such decelerations are common within the
foreshock and are caused by the interaction of the solar wind with
backstreaming ions which slow down the incoming solar wind by
transferring the momentum flux [Bame et al., 1980; Bonifazi et al.,
1980; see also the review by Thomsen, 1985]. Thus varying IMF direction
can modify the geometry of the foreshock and alter the distribution of
pressure on the magnetopause. In this way IMF directional fluctuations
can cause compressions of the magnetosphere and may explain some
pressure pulses seen there.

Coherence Length of ULF Waves

ULF waves are carried downstream towards the bow shock and magnetopause
along solar wind streamlines and modulate the structures of both the bow
shock and the magnetopause if they have sufficient amplitude and scale
size. The coherence length of the ULF waves has been investigated using
simultaneous observations from the dual ISEE 1 and 2 spacecraft [Le and
Russell, 1990a]. In that study, we examined the correlation between
these simultaneous observations for different separations of the two
spacecraft.
Figure 10
shows the cross-correlation coefficients as a
function of separation distance perpendicular to the solar wind flow
where each line corresponds to a different separation parallel to the
solar wind flow. The cross-correlation coefficients decrease as the
separation perpendicular to the flow increases. However the
cross-correlation coefficients are similar despite different separations
along the solar wind flow. The coherence length is on the order of an
Earth radius transverse to the solar wind flow, a scale similar to the
wavelength. This result is consistent with that estimated from the
bandwidth of the power spectra. The limited coherence length in the
direction transverse to the flow is mainly due to the solar wind
convection effect. In the direction along the solar wind flow, the
coherence length is at least several Earth radii. Thus, ULF waves are
large-scale coherent structures, and should induce similar scale-size
coherent oscillations in the bow shock and magnetopause, and in turn in
the magnetosphere itself.

Bandwidth of ULF Waves

The ULF foreshock modifies the turbulence spectrum convected downstream
to the magnetopause. Thus, in order to predict the magnetospheric
effects of these waves it is of interest to determine the frequency
range of enhanced power of magnetic fluctuations in the foreshock
region. We have compared the ULF wave power spectrum with the background
solar wind spectrum and found that the enhanced wave power has limited
bandwidth [Le and Russell, 1990b]. In that study, simultaneous
observations from two largely separated spacecraft that are located on
either side of the ULF foreshock were examined. The data indicate that
the foreshock ULF wave power spectrum has a clear low-frequency cutoff,
below which the power spectra are similar in the undisturbed solar wind
and in the foreshock. This low-frequency cutoff occurs above ~ 5 mHz.
Figure 11
shows one example in which ISEE 1 is inside the foreshock and
IMP-8 is in the undisturbed solar wind. From this figure it is apparent
that ISEE 1 observes enhanced power at frequencies higher than 7 mHz.
There is no significant power enhancement or damping below 7 mHz. This
result does not support the suggestion that upstream shock-related
pressure oscillations drive magnetopause surface waves and
magnetospheric oscillations with periods of ~ 200-600 seconds
[Sibeck et al., 1989].

In short the solar wind flow is significantly perturbed in the foreshock
region. The perturbation is unsteady due to frequent variations of IMF
orientations, perhaps explaining some pressure pulses in the
magnetosphere. Wave processes in the foreshock are however band limited
and thus can be directly responsible for only a fraction of the waves in
the magnetosphere.

5. SPATIAL VARIATION OF ULF WAVES

It is well known that the properties of upstream ULF waves are position
dependent within the foreshock and the waveform varies from nearly
sinusoidal to highly steepened as the
increases [Hoppe et al., 1981;
Russell et al., 1987]. The region populated by the intermediate ions is
the forward boundary of the ULF wave foreshock. The waves there are
fairly monochromatic and typically last many cycles. They are
left-handed polarized in the spacecraft frame. Further downstream from
the ULF foreshock boundary in the region populated by diffuse ions, the
ULF waves often appear in the form of the steepened shocklets. They
exhibit both left-handed and right-handed polarization in the spacecraft
frame, and the left-handed and right-handed waves are similar in form,
frequency, and wavelength.

Russell et al. [1987] used simultaneous observations from two well
separated spacecraft to show that the properties of the ULF waves depend
on the their location in the foreshock region. The properties include
waveform, amplitude, polarization and power spectrum. Early observations
of backstreaming ions also revealed that the properties of backstreaming
ions varied with respect to point of origin along the bow shock
[Paschmann et al., 1981; Ipavich et al., 1981; Thomsen, 1985].

Since solar wind conditions, especially the IMF direction, are highly
variable, early observations of the ULF waves were made under various
solar wind conditions and did not reveal the structure of the region
behind the foreshock boundary, or spatial variation of ULF waves within
this region. When the IMF cone angle changes, the foreshock geometry
changes accordingly. Thus it is essential to study the evolution of ULF
waves under similar conditions of IMF and bow shock strength, which is
another controlling factor. During a long interval of nearly constant
solar wind conditions, the motion of backstreaming ions can reach a
nearly steady state, as do the waves generated by them. In this case,
the changes of wave properties are primarily related to the geometry in
the foreshock, i.e., the different depth from the foreshock boundary and
distance from the bow shock.

We have examined cases in which the IMF cone angle was nearly constant
over an extended time period and ISEE 1 and 2 spacecraft were traveling
a large distance within the foreshock [Le and Russell, 1992b].
Figure 12
shows one of the cases examined. The top panel shows the foreshock
geometry and ISEE trajectory in the V-B plane. The lower panels show the
magnetic field data during this interval. Large-amplitude ULF waves with
periods near 40 seconds were present throughout this interval and these
ULF waves exhibited predominantly a steepened form (shocklets). The
amplitudes of the waves increase gradually as the spacecraft travels to
large depth from the foreshock boundary and closer to the bow shock.
Following the increase of wave amplitude, the waves vary from
elliptically polarized to more linearly polarized. The wave power
spectra
(Figure 13) shows that the peak of power spectrum became broader
towards both lower and higher frequencies while the peak frequency
stayed nearly the same as the bow shock is approached. In addition the
spectra had a limited bandwidth and a clear low frequency cutoff
throughout the interval.

From the bottom panels of Figure 12, it is evident that the discrete
wave packets found at the steepening edges of the lower-frequency waves,
or shocklets, become more intense and develop more cycles associated
with the increasing intensity of the shocklets.
Figure 14
shows the wave
duration in cycles and the peak-to-peak amplitude of the discrete wave
packets (the largest cycle) as a function of distance from the bow shock
along a solar wind streamline. The scale length given by the exponential
fit is 1.9 Re for the wave duration and 2.8 Re for the wave amplitude.
Based on the facts that these wave packets were convected downstream
with the solar wind and that their phase velocity was much less than the
solar wind velocity, the estimated growth rate for the discrete wave
packets was ~ 0.035 for the particular geometry and solar wind
conditions of this interval.

6. REMAINING PROBLEMS

Despite intensive studies of the upstream waves over the past two
decades, there are still many remaining problems which need further
investigation. First of all, the present theoretical models for wave
generation are not successful in predicting all the properties of
observed ULF waves. From the linear theories the maximum growth rates
for all three instabilities always occur for parallel propagation (k//B)
over all parameter space, although the growth rate for oblique
propagation waves can be significant [Montgomery et al., 1976; Gary,
1991]. However, the large-amplitude ULF waves are observed as highly
compressional and steepening. Thus they propagate obliquely to the
magnetic field. Hada et al. [1987] proposed a refraction mechanism to
account for the observed obliquely propagating waves. In their mechanism
the parallel propagating right-handed and left-handed waves are excited
by the backstreaming ions in the upstream region. These waves are
refracted to oblique propagation as they are convected downstream by the
solar wind due to the non-uniform index of refraction caused by the
spatial variation of the backstreaming ions. As a result, the waves
become compressional and steepen into the shocklets. In this mechanism,
geometry is very important and shocklets should not be observed in the
nearly radial IMF geometry because the effect of refraction is minimum
for parallel propagating waves. However, we have shown evidence that
both shocklets and discrete wave packets are observed when the IMF is
nearly radial (Figure 6). The linear theories also predict that ULF
waves exhibit both left-handed and right-handed polarization in the
spacecraft frame. Observations have shown that polarization and wave
amplitude are correlated. For the right-handed waves in the spacecraft
frame, their intrinsic mode can be either right-handed or left-handed.
Thus the identification of the intrinsic mode and conditions for which
they occur will help us to understand their generation mechanisms.

Solving these problems also relies largely on a better understanding of
upstream particles. Combined data sets from many instruments (both field
and plasma) will provide detailed information on the physics of the
underlying processes. This is still a weak point in the foreshock study
despite of the fact that existing ISEE data sets with high time
resolution are available for over a decade. Previous work used either
primarily magnetic field data or primarily plasma data to study the
morphology of the foreshock region and the spatial variation of waves
properties. For example, previous attempts to determine the ULF
foreshock boundary were mainly based on field observations and
properties of the backstreaming ions were inferred from these
observations. However, we do not know the behavior of the backstreaming
ions near the foreshock boundary identified from field data. Do the
backstreaming ions move upstream at a velocity inferred from magnetic
field observations? What is the difference, if any, between the
boundaries of backstreaming ions and ULF waves and how does the
backstreaming ion distribution function change across the ULF wave
boundary? We note that the growth of waves in the unstable
backstreaming ions is not instantaneous and in fact waves grow in a
parcel of plasma as it convects towards the bow shock. The onset of
waves may not simply reflect the variation in backstreaming ion
properties. We studied the spatial variation of ULF waves under steady
solar wind conditions, but we do not know the spatial variation of the
backstreaming ions under
these conditions. We do not know how the change of wave properties
depends on the change of streaming velocity, density, and distribution
function of the backstreaming ions.

The importance of upstream phenomena is not limited to the Earth's
upstream region. The comparative study of a variety of foreshocks is
very important for understanding the underlying physical processes.
Waves have been observed upstream from bow shocks of Mercury, Venus,
Mars, Jupiter, Saturn and Uranus. Their similarities and differences are
not currently very well understood. First, the solar wind Mach number
increases with increasing heliocentric
distance. The significant increases in the strength of planetary shocks
with increasing distance from the sun may induce considerable changes in
the relative efficiencies of the various processes such as leakage and
reflection that generate the backstreaming ions. Another important
factor that may influence the wave and particle
signatures observed in the upstream region is the varying time of
connection of the field lines to the planetary shock and the varying
radius of curvature of the bow shock relative to characteristic scale
lengths, (eg., the proton gyroradius and ion inertial length). For the
above reasons it is essential to study a variety of foreshocks and to
determine the dependence of the microphysics of the foreshock phenomena
on varying
boundary conditions.

Acknowledgments. This work was supported by the National Aeronautics and
Space Administration under research grant NAGW-2067.

Figure 5.
The spacecraft positions at the ULF foreshock boundary crossings
for 50 +/- 5 cone angles are plotted in the V-B plane. The bow shock is
scaled by the solar wind dynamic pressure and the magnetosonic Mach
number, and then, normalized to the same size for each crossings.
(Adapted from Le and Russell [1992a])

Figure 7.
The upper panel is the normalized ULF wave spectral amplitude as
a function of the distance from the bow shock for nearly radial IMF. The
solid line is a linear fit to the data and the dotted line is an
exponential fit. The lower panel is the data coverage in the plane
containing the spacecraft and the Earth-Sun line. (Adapted from Le
[1991])

Figure 8.
The wave ellipticity versus the normalized amplitude for nearly
radial IMF. The correlation coefficient is 0.57, which is significant at
almost 100% level. (Adapted from Le [1991])

Figure 9.
The time series of magnetic field components, magnetic field
strength, ion density, bulk velocity, and dynamic pressure from 0630 to
1130 UT on December 6, 1977. The IMF changes its direction near 0825 UT.
There are enhanced fluctuations in ion density and dynamic pressure
associated with the ULF waves. (Adapted rom Le [1991])

Figure 10.
The cross-correlation coefficients as a function of spacecraft
separation perpendicular to the solar wind flow for each 0.1 RE
separation parallel to the solar wind flow. (Adapted from Le and Russell
[1990a])

Figure 11.
The magnetic field time series, power spectra, and foreshock
geometry from simultaneous observations of ISEE 1 and IMP-8 on November
1, 1981. (Adapted from Le and Russell [1990b])

Figure 12.
The upper panel shows the ISEE trajectory in the V-B plane from
1400 to 2100 UT on September 4, 1983 when the IMF cone angle was nearly
constant over an extended time period. The lower panels are magnetic
field observations. (Adapted from Le and Russell [1992b])

Figure 13.
The power spectra of 32--minute magnetic field data with
starting times indicated in the figure on September 4, 1983. Each
spectrum is the total power summed over three components, and is plotted
by shifting one decade upward from the previous one. (Adapted from Le
and Russell [1992b])

Figure 14.
The spatial variation of the duration and the peak-to-peak
amplitude of discrete wave packets on September 4, 1983. (Adapted from
Le and Russell [1992b])